Systems and Methods for Processing Acoustic Cement Evaluation Data

ABSTRACT

Systems, methods, and devices for evaluating proper cement installation in a well are provided. In one example, a method includes obtaining acoustic cement evaluation data points and processing the acoustic cement evaluation data points using a solid-liquid-gas model to assign at least some of the acoustic cement evaluation data points to a material of solid, liquid, or gas in an annulus of the wellbore behind the casing. The solid-liquid-gas model includes a tight solid-liquid-gas model in which a gas threshold range is not directly adjacent to a liquid threshold range and/or a solid-liquid-gas model that considers flexural attenuation when a pulse-echo-derived acoustic impedance is below an evanescence point.

BACKGROUND

This disclosure relates to evaluating cement behind a casing of awellbore and, or particularly, to cement evaluation data processingassociated with a solid-liquid-gas (SLG) model map.

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the present techniques,which are described and/or claimed below. This discussion is believed tobe helpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentdisclosure. Accordingly, it should be understood that these statementsare to be read in this light.

A wellbore drilled into a geological formation may be targeted toproduce oil and/or gas from certain zones of the geological formation.To prevent zones from interacting with one another via the wellbore andto prevent fluids from undesired zones entering the wellbore, thewellbore may be completed by placing a cylindrical casing into thewellbore and cementing the annulus between the casing and the wall ofthe wellbore. During cementing, cement may be injected into the annulusformed between the cylindrical casing and the geological formation. Whenthe cement properly sets, fluids from one zone of the geologicalformation may not be able to pass through the wellbore to interact withone another. This desirable condition is referred to as “zonalisolation.” Yet well completions may not go as planned. For example, thecement may not set as planned and/or the quality of the cement may beless than expected. In other cases, the cement may unexpectedly fail toset above a certain depth due to natural fissures in the formation.

A variety of acoustic tools may be used to verify that cement isproperly installed. These acoustic tools may use pulsed acoustic wavesas they are lowered through the wellbore to obtain acoustic cementevaluation data (e.g., flexural attenuation and/or acoustic impedancemeasurements). A solid-liquid-gas (SLG) model map may be used tointerpret the acoustic cement evaluation data to indicate whethersolids, liquids, or gases are in the annulus behind the casing of thewellbore. When the SLG model map indicates that a solid is present, thecement is likely to have set properly. When the SLG model map indicatesthat a liquid or gas is present, the cement may be interpreted not tohave properly set or otherwise may not be seen. Although the SLG modelmap can be used to map acoustic measurements to a probabilistic state ofthe material behind the casing (e.g., solid, liquid, or gas), certainwell logging conditions, such as light cement, can challenge theeffectiveness of the SLG model map.

SUMMARY

A summary of certain embodiments disclosed herein is set forth below. Itshould be understood that these aspects are presented merely to providethe reader with a brief summary of these certain embodiments and thatthese aspects are not intended to limit the scope of this disclosure.Indeed, this disclosure may encompass a variety of aspects that may notbe set forth below.

Embodiments of this disclosure relate to various systems, methods, anddevices for evaluating proper cement installation in a well. Thus, thesystems, methods, and devices of this disclosure describe various waysof using acoustic cement evaluation data obtained from acoustic downholetools to identify when a material behind a casing in a well is likely tobe a solid, liquid, or gas. In one example, a method includes obtainingacoustic cement evaluation data points and processing the acousticcement evaluation data points using a solid-liquid-gas model to assignat least some of the acoustic cement evaluation data points to amaterial of solid, liquid, or gas in an annulus of the wellbore behindthe casing. The solid-liquid-gas model includes a tight solid-liquid-gasmodel in which a gas threshold range is not directly adjacent to aliquid threshold range and/or a solid-liquid-gas model that considersflexural attenuation when a pulse-echo-derived acoustic impedance isbelow an evanescence point.

In another example, computer-readable media may store instructions toreceive data points—each data point including a first component based onmeasured flexural attenuation and a second component based onpulse-echo-derived acoustic impedance—and assign at least some datapoints having a second component value at or above an evanescence pointto indicate that a material behind the casing is solid. The instructionsalso include, depending at least in part on a value of the firstcomponent, instructions to assign at least some data points having asecond component value below the evanescence point to indicate that thematerial behind the casing is solid, liquid, or gas.

In another example, a method includes receiving acoustic cementevaluation data points, processing the acoustic cement evaluation datapoints using an initial solid-liquid-gas model, and performing aposteriori refinement of the initial solid-liquid-gas model to determinea refined solid-liquid-gas model that is more precise or more accurate,or more precise and more accurate, than the initial solid-liquid-gasmodel. The acoustic cement evaluation data points then may be processedusing the refined solid-liquid-gas model.

Various refinements of the features noted above may be undertaken inrelation to various aspects of the present disclosure. Further featuresmay also be incorporated in these various aspects as well. Theserefinements and additional features may be determined individually or inany combination. For instance, various features discussed below inrelation to the illustrated embodiments may be incorporated into any ofthe above-described aspects of the present disclosure alone or in anycombination. The brief summary presented above is intended tofamiliarize the reader with certain aspects and contexts of embodimentsof the present disclosure without limitation to the claimed subjectmatter.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of this disclosure may be better understood upon readingthe following detailed description and upon reference to the drawings inwhich:

FIG. 1 is a schematic diagram of a system for verifying proper cementinstallation and/or zonal isolation of a well, in accordance with anembodiment;

FIG. 2 is a block diagram of an acoustic downhole tool to obtainacoustic cement evaluation data relating to material behind casing ofthe well, in accordance with an embodiment;

FIG. 3 is a flowchart of a method for interpreting the acoustic cementevaluation data, which may include a parametric correction, processingvia a tight or flexural-evanescence-acoustic-impedance (Flex-EVA-AI)solid-liquid-gas (SLG) model, and/or posteriori model refinement, inaccordance with an embodiment;

FIG. 4 is a flowchart for performing a parametric correction of theacoustic cement evaluation data, in accordance with an embodiment;

FIG. 5 is a plot illustrating a relationship between flexuralattenuation and acoustic impedance measurements obtained in a well, inaccordance with an embodiment;

FIG. 6 is a plot of flexural attenuation and acoustic impedance datapoints in an x-y density distribution, in accordance with an embodiment;

FIG. 7 is an example of a conservative solid-liquid-gas (SLG) model map,in accordance with an embodiment;

FIG. 8 is a plot showing a transformation of the conservative SLG modelmap of FIG. 7 using flexural attenuation data transformed into acousticimpedance data, in accordance with an embodiment;

FIG. 9 is a flowchart of a method for determining when parametriccorrection is warranted by comparing actual acoustic cement evaluationdata to expected behavior of the cement evaluation data, in accordancewith an embodiment;

FIG. 10 is a flowchart of a method for ensuring the correction of theacoustic cement evaluation data to more closely resemble the expectedcement evaluation data, in accordance with an embodiment;

FIG. 11 is an example plot showing a way of correcting acoustic cementevaluation data points to more closely match expected nominal values, inaccordance with an embodiment;

FIGS. 12 and 13 are plots of actual acoustic cement evaluation datapoints that are parametrically corrected to more closely match expectednominal values, in accordance with an embodiment;

FIG. 14 is a flowchart of a method for correcting acoustic cementevaluation data having flexural attenuation or acoustic impedancemeasurements, in accordance with an embodiment;

FIG. 15 is a flowchart of a method for parametrically correcting theacoustic cement evaluation data of FIG. 14, in accordance with anembodiment;

FIG. 16 is a plot of data points used to develop a solid-liquid-gas(SLG) model map when the data points used in a computer model, inaccordance with an embodiment;

FIG. 17 is a plot of data points that may be used to generate theconservative SLG model map of FIG. 7 by using a first noise estimatepropagated through a computer model, in accordance with an embodiment;

FIG. 18 is an example of a Flex-EVA-AI solid-liquid-gas (SLG) model mapthat uses flexural attenuation to classify solids, liquids, and gaseswhen acoustic impedance is below an evanescence point, in accordancewith an embodiment;

FIG. 19 is a flowchart of a method for using the Flex-EVA-AI SLG modelmap of FIG. 18, in accordance with an embodiment;

FIG. 20 illustrates three well log tracks: one generated using theconservative SLG model map, one generated using the Flex-EVA-AI SLGmodel map of FIG. 18, and one of acoustic impedance data, in accordancewith an embodiment;

FIG. 21 is a “tight” solid-liquid-gas (SLG) model map that uses tightertolerances than the conservative SLG model map and may separate a liquidrange from a gas range and the liquid range from a light solid range, inaccordance with an embodiment;

FIG. 22 is a plot of data points that may be used to generate the tightSLG model map of FIG. 21 by using a tighter noise estimate propagatedthrough a computer model, in accordance with an embodiment;

FIGS. 23 and 24 are flowcharts of methods for performing posterioricorrection of acoustic cement evaluation data, in accordance withembodiments;

FIG. 25 is an example density plot of acoustic cement evaluation dataoverlaid on a conservative SLG model map, in accordance with anembodiment; and

FIG. 26 is an example density plot of the same acoustic cementevaluation data overlaid on the “tight” SLG model map of FIG. 21, whichprovides a better fit under these circumstances, in accordance with anembodiment.

DETAILED DESCRIPTION

One or more specific embodiments of the present disclosure will bedescribed below. These described embodiments are examples of thepresently disclosed techniques. Additionally, in an effort to provide aconcise description of these embodiments, some features of an actualimplementation may not be described in the specification. It should beappreciated that in the development of any such actual implementation,as in any engineering or design project, numerousimplementation-specific decisions may be made to achieve the developers'specific goals, such as compliance with system-related andbusiness-related constraints, which may vary from one implementation toanother. Moreover, it should be appreciated that such a developmenteffort might be complex and time consuming, but would still be a routineundertaking of design, fabrication, and manufacture for those ofordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the presentdisclosure, the articles “a,” “an,” and “the” are intended to mean thatthere are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.Additionally, it should be understood that references to “oneembodiment” or “an embodiment” of the present disclosure are notintended to be interpreted as excluding the existence of additionalembodiments that also incorporate the recited features.

When a well is drilled, metal casing may be installed inside the welland cement placed into the annulus between the casing and the wellbore.When the cement sets, fluids from one zone of the geological formationmay not be able to pass through the annulus of the wellbore to interactwith another zone. This desirable condition is referred to as “zonalisolation.” Proper cement installation may also ensure that the wellproduces from targeted zones of interest. To verify that the cement hasbeen properly installed, this disclosure teaches systems and methods forevaluating acoustic cement evaluation data. As used herein, “acousticcement evaluation data” refers to acoustic impedance data and/orflexural attenuation data that may be obtained from one or more acousticdownhole tools.

The acoustic cement evaluation data may that is obtained by the acousticdownhole tools may be parameterized based on initial assumptions on thecharacteristics of the well and/or the acoustic downhole tools. Forinstance, the acoustic cement evaluation data may include an assumedtype of liquid that may displace the cement in the annulus of the well(e.g., water or a hydrocarbon fluid) and/or a flexural attenuationcalibration. Yet errors in these initial parameters could incorrectlypredict the actual conditions in the well. As a result, the acousticcement evaluation data may not accurately reflect the true conditions ofthe well. In addition, properties of different wells may not be wellsuited to a conservative solid-liquid-gas (SLG) model map used toidentify whether a solid, liquid, or gas is likely in the annulus behindthe casing. Before continuing, a “conservative” SLG model map, asreferred to herein, represents an SLG model map that may discriminatebetween liquid, solid, and gas using acoustic cement evaluation data. Anexample of the conservative SLG model map will discussed below withreference to FIGS. 7, 16, and 17. In general, a conservative SLG modelmap may be obtained by a computer model that, given certain a prioriparametric and/or data noise estimates, may develop the SLG model mapbased on this a priori information. In this way, SLG model maps may beunique to selected a priori parameters relating to the well, which mayinclude nominal casing thickness. The a priori parametric and/or datanoise estimates used to generate the conservative SLG model map 160 maybe any suitable parametric and/or data noise estimates that, based oncollections of empirical data from various wells, would be understood toconservatively classify acoustic cement evaluation data points assolids, liquids, and gases.

This disclosure teaches various ways to improve the results obtainedfrom acoustic cement evaluation data. For instance, the initial acousticcement evaluation data may be parametrically corrected to account forerrors in parameter assumption, other solid-liquid-gas (SLG) models maybe used, and/or SLG models may undergo posteriori refinement based onthe actual acoustic cement evaluation data as it is applied to the SLGmodels. In essence, the disclosure relates to multimode processing andprocessing of independent acoustic measurements to determine whether asolid, liquid, or gas is likely to be present behind a casing of a well.

With this in mind, FIG. 1 schematically illustrates a system 10 forevaluating cement behind casing in a well. In particular, FIG. 1illustrates surface equipment 12 above a geological formation 14. In theexample of FIG. 1, a drilling operation has previously been carried outto drill a wellbore 16. In addition, an annular fill 18 (e.g., cement)has been used to seal an annulus 20—the space between the wellbore 16and casing joints 22 and collars 24—with cementing operations.

As seen in FIG. 1, several casing joints 22 (also referred to below ascasing 22) are coupled together by the casing collars 24 to stabilizethe wellbore 16. The casing joints 22 represent lengths of pipe, whichmay be formed from steel or similar materials. In one example, thecasing joints 22 each may be approximately 13 m or 40 ft long, and mayinclude an externally threaded (male thread form) connection at eachend. A corresponding internally threaded (female thread form) connectionin the casing collars 24 may connect two nearby casing joints 22.Coupled in this way, the casing joints 22 may be assembled to form acasing string to a suitable length and specification for the wellbore16. The casing joints 22 and/or collars 24 may be made of carbon steel,stainless steel, or other suitable materials to withstand a variety offorces, such as collapse, burst, and tensile failure, as well aschemically aggressive fluid.

The surface equipment 12 may carry out various well logging operationsto detect conditions of the wellbore 16. The well logging operations maymeasure parameters of the geological formation 14 (e.g., resistivity orporosity) and/or the wellbore 16 (e.g., temperature, pressure, fluidtype, or fluid flowrate). Other measurements may provide acoustic cementevaluation data (e.g., flexural attenuation and/or acoustic impedance)that may be used to verify the cement installation and the zonalisolation of the wellbore 16. One or more acoustic logging tools 26 mayobtain some of these measurements.

The example of FIG. 1 shows the acoustic logging tool 26 being conveyedthrough the wellbore 16 by a cable 28. Such a cable 28 may be amechanical cable, an electrical cable, or an electro-optical cable thatincludes a fiber line protected against the harsh environment of thewellbore 16. In other examples, however, the acoustic logging tool 26may be conveyed using any other suitable conveyance, such as coiledtubing. The acoustic logging tool 26 may be, for example, an UltraSonicImager (USI) tool and/or an Isolation Scanner (IS) tool by SchlumbergerTechnology Corporation. The acoustic logging tool 26 may obtainmeasurements of acoustic impedance from ultrasonic waves and/or flexuralattenuation. For instance, the acoustic logging tool 26 may obtain apulse echo measurement that exploits the thickness mode (e.g., in themanner of an ultrasonic imaging tool) or may perform a pitch-catchmeasurement that exploits the flexural mode (e.g., in the manner of animaging-behind-casing (IBC) tool). These measurements may be used asacoustic cement evaluation data in a solid-liquid-gas (SLG) model map toidentify likely locations where solid, liquid, or gas is located in theannulus 20 behind the casing 22.

The acoustic logging tool 26 may be deployed inside the wellbore 16 bythe surface equipment 12, which may include a vehicle 30 and a deployingsystem such as a drilling rig 32. Data related to the geologicalformation 14 or the wellbore 16 gathered by the acoustic logging tool 26may be transmitted to the surface, and/or stored in the acoustic loggingtool 26 for later processing and analysis. As will be discussed furtherbelow, the vehicle 30 may be fitted with or may communicate with acomputer and software to perform data collection and analysis.

FIG. 1 also schematically illustrates a magnified view of a portion ofthe cased wellbore 16. As mentioned above, the acoustic logging tool 26may obtain acoustic cement evaluation data relating to the presence ofsolids, liquids, or gases behind the casing 22. For instance, theacoustic logging tool 26 may obtain measures of acoustic impedanceand/or flexural attenuation, which may be used to determine where thematerial behind the casing 22 is a solid (e.g., properly set cement) oris not solid (e.g., is a liquid or a gas). When the acoustic loggingtool 26 provides such measurements to the surface equipment 12 (e.g.,through the cable 28), the surface equipment 12 may pass themeasurements as acoustic cement evaluation data 36 to a data processingsystem 38 that includes a processor 40, memory 42, storage 44, and/or adisplay 46. In other examples, the acoustic cement evaluation data 36may be processed by a similar data processing system 38 at any othersuitable location. The data processing system 38 may collect theacoustic cement evaluation data 36 and determine whether such data 36represents a solid, liquid, or gas using a solid-liquid-gas (SLG) modelmap. Additionally or alternatively, the data processing system 38 mayperform a parametric correction of the acoustic cement evaluation data36, may apply the data 36 to one or more different SLG models, and/ormay perform a posteriori refinement of the SLG model. To do this, theprocessor 40 may execute instructions stored in the memory 42 and/orstorage 44. As such, the memory 42 and/or the storage 44 of the dataprocessing system 38 may be any suitable article of manufacture that canstore the instructions. The memory 42 and/or the storage 44 may be ROMmemory, random-access memory (RAM), flash memory, an optical storagemedium, or a hard disk drive, to name a few examples. The display 46 maybe any suitable electronic display that can display the logs and/orother information relating to classifying the material in the annulus 20behind the casing 22.

In this way, the acoustic cement evaluation data 36 from the acousticlogging tool 26 may be used to determine whether cement of the annularfill 18 has been installed as expected. In some cases, the acousticcement evaluation data 36 may indicate that the cement of the annularfill 18 has a generally solid character (e.g., as indicated at numeral48) and therefore has properly set. In other cases, the acoustic cementevaluation data 36 may indicate the potential absence of cement or thatthe annular fill 18 has a generally liquid or gas character (e.g., asindicated at numeral 50), which may imply that the cement of the annularfill 18 has not properly set. For example, when the indicate the annularfill 18 has the generally liquid character as indicated at numeral 50,this may imply that the cement is either absent or was of the wrong typeor consistency, and/or that fluid channels have formed in the cement ofthe annular fill 18. By processing the acoustic cement evaluation data36, ascertaining the character of the annular fill 18 may be moreaccurate and/or precise than merely using the data 36 in a conservativeSLG model map.

With this in mind, FIG. 2 provides a general example of the operation ofthe acoustic logging tool 26 in the wellbore 16. Specifically, atransducer 54 in the acoustic logging tool 26 may emit acoustic waves 54out toward the casing 22. Reflected waves 56, 58, and 60 may correspondto interfaces at the casing 22, the annular fill 18, and the geologicalformation 14 or an outer casing, respectively. The reflected waves 56,58, and 60 may vary depending on whether the annular fill 18 is of thegenerally solid character 48 or the generally liquid or gas character50. The acoustic logging tool 26 may use any suitable number ofdifferent techniques, including measurements of acoustic impedance fromultrasonic waves and/or flexural attenuation. As used below, the term“FA” refers to measured flexural attenuation, “AI” and “Z(AI)” refer topulse-echo-derived acoustic impedance, and “Z(FA)” or“flexural-attenuation-derived acoustic impedance” refer to a calculationof acoustic impedance determined based on the flexural attenuationmeasurement. Various of these measurements obtained at the same depth inthe wellbore 16 may be correlated to gain insight into the properties ofthe material behind the casing 22. These may be, for example, “FA-AI”data points, which relate flexural attenuation and pulse-echo-derivedacoustic impedance, or “AI-AI” data points, which relateflexural-attenuation-derived acoustic impedance and pulse-echo-derivedacoustic impedance. When one or more of these measurements of acousticcement evaluation data are obtained, they may be parameterized based oninitial assumptions on the characteristics of the well and/or theacoustic downhole tools. For instance, the acoustic cement evaluationdata may include an assumed type of liquid that may displace the cementin the annulus of the well (e.g., water or a hydrocarbon fluid) and/or aflexural attenuation calibration. Yet it may be appreciated that theseinitial parameters could incorrectly predict the actual conditions inthe well.

In any case, the acoustic cement evaluation data may be processed invarious ways to achieve a final solid-liquid-gas (SLG) answer product.For instance, as shown by a flowchart 70 of FIG. 3, the acoustic cementevaluation data points may be obtained by measurements using one or moreacoustic tools 26 (block 72). These acoustic cement evaluation datapoints may include, for example, acoustic impedance data, flexuralattenuation data, or both.

The acoustic cement evaluation data may or may not warrant or undergoparametric correction (block 74). When the acoustic cement evaluationdata is parametrically corrected, a self correction scheme (block 76) ora manual correction scheme (block 78) may be used in a correction of oneor both of acoustic impedance or flexural attenuation measurements ofthe acoustic cement evaluation data. The parametric correction of block74 will be described below with reference to FIGS. 4-15.

Whether or not the acoustic cement evaluation data is parametricallycorrected, the data may be used for processing in one or more a priorisolid-liquid-gas (SLG) models (block 80). This may include aconservative solid-liquid-gas (SLG) model 82, a “tight” SLG model 84,and/or a flexural attenuation-acoustic impedance SLG model 86 thatexpressly takes the evanescence point of the acoustic impedance intoconsideration. Processing using these a priori models of block 80 willbe described below with reference to FIGS. 16-22.

If desired, the data processing system 38 may conduct posteriorirefinement of one or more of the SLG models by comparing the way inwhich the actually obtained acoustic cement evaluation data fits intothe SLG models (block 88). In some examples, this refinement may takeplace in a one-dimensional manner (block 90) or a two-dimensional manner(block 92). The posteriori model refinement of block 88 will bedescribed below with reference to FIGS. 23-26.

The data processing system 38 may provide a solid-liquid-gas (SLG)answer product using the SLG model maps of block 80 or the refined modelmap of block 88 (block 94). The answer product may include a well logthat particularly discriminates solid, liquid, and/or gas that is likelyto be behind the casing 22. Before continuing, it should be appreciatedthat the flowchart 70 of FIG. 3 is merely intended to provide an exampleprocess. In other examples, just some of the blocks discussed above maybe carried out. In one embodiment, for example, the parametriccorrection of block 74 may be carried out but the posteriori refinementof block 88 may not. Indeed, any combination of the above acts may becarried out as desired.

Parametric Correction

The raw information obtained from the acoustic tool(s) 26 may beparameterized using an initial parameterization. This initialparameterization may include, for example, a calibration of flexuralattenuation (sometimes referred to as UFAO) and/or an expected acousticimpedance Z of the fluid in the wellbore 16. While databases may be usedto help guide the initial parameterization, it may not be unusual to seeparameter errors that can affect the ultimate interpretation of theacoustic cement evaluation data. As such, the acoustic cement evaluationdata may be parametrically corrected before being interpreted in asolid-liquid-gas (SLG) model map.

As will be discussed below, when the acoustic cement evaluation dataincludes both flexural attenuation data and acoustic impedance data,there are certain relationships between these different measurementsthat may inform when parameterization errors have occurred. Theparameterization errors may be corrected by reprocessing with newcorrected parameters or by directly correcting the acoustic cementevaluation data. FIGS. 4-13 relate to such a two-measurement approach,which is also referred to below as an x-y density distribution approach.FIGS. 14 and 15 relate to a similar one-measurement parametriccorrection to make a correction of the flexural attenuation or acousticimpedance data separately.

Parametric Correction Using Flexural Attenuation-Acoustic ImpedanceRelationship

A flowchart 100 of FIG. 4 illustrates a two-measurement, x-y densitydistribution approach to make a parametric correction of the acousticcement evaluation data. In the flowchart 100 of FIG. 4, the dataprocessing system 38 may consider a relationship betweenpulse-echo-derived acoustic impedance data and acoustic impedance valuesderived from measured flexural attenuation values, which are referred toin this disclosure as AI-AI or Z(FA)-Z(AI) values or data points (block102). Points beneath an evanescence point may be used for the analysisleading to parameter correction. These points beneath the evanescencepoint may be referred to as a “subset” of the entire dataset of datapoints. Once estimated, the correction can be applied to the entiredataset or some portion of the entire dataset, regardless of whether thepoints in the entire dataset or the portion of the entire dataset areabove or below the evanescence point. The significance of theevanescence point and the transformation of the flexural attenuationdata into second acoustic impedance data will be described below.

The data processing system may investigate the resulting AI-AIpopulation distribution in the resulting x-y density distribution (block104). The data processing system 38 may perform parametric correction onthe AI-AI population of the x-y density distribution to fit centroids ofthe data to certain expected nominal anchor points (block 106). Thisprocess, and its ultimate results, will be described in greater detailbelow.

Indeed, FIG. 5 is a plot 110 that relates flexural attenuation (FA) inunits of dB/cm (ordinate 112) to acoustic impedance (AI) in units ofMRayls (abscissa 114). This relationship may be referred to as an FA-AIrelationship. The measurements are shown to be test measurementsobtained using a steel plate with an 8 mm thickness to simulate a casing22. A curve 116 illustrates the relationship between experimental valvesof flexural attenuation and acoustic impedance for known materialsbehind the steel plate that simulates the casing 22. As seen in FIG. 5,the curve 116 progresses in a substantially linear manner until reachingevanescence point 118 in the acoustic impedance. For acoustic impedancevalues beyond the evanescence point 118, the flexural attenuation nolonger enjoys the same linear relationship, as illustrated by a curve126. The evanescence point 118 represents the transition from a solidthat is able to maintain both a compressional and shear propagation tothat of just shear propagation.

A point 120, in which the flexural attenuation and acoustic impedanceare around values of approximately zero, represents gas behind the steelplate that stimulates the casing 22. Thus, when the acoustic impedanceand flexural attenuation both have values around zero, this implies thata gas is likely behind the casing 22. A point 122 generally representsliquid behind the steel plate that simulates the casing 22. In theexample of FIG. 5, the point 122 represents a point where water isbehind the steel plate that simulates the casing 22. Around an area 124,the acoustic impedance and flexural attenuation values begin tocorrespond to a solid (e.g., cement), rather than a liquid, behind thesteel plate that simulates the casing 22 in the plot 110. Beyond theevanescence point 118, shown also to be impedance (Z), the materialbehind the steel plate that simulates the casing 22 is understood to bea solid.

As discussed above, there is linearity in the relationship betweenflexural attenuation and acoustic impedance up to the evanescence point118 of the acoustic impedance. Indeed, the FA-AI measurement of gas,liquids, and light solids may fall below the evanescence limit 118 andhave a linear slope as shown along the curve 116. Solids behind thecasing 22 may have a wide range of FA-AI values. Liquids, which mayresult from displaced drilling muds and spacer fluids, may also vary inFA-AI values. Meanwhile, gas has a very tight, well-defined, andwell-understood behavior of acoustic impedance, generally fallingprimarily along values near 0 for both flexural attenuation and acousticimpedance. Thus, for the subset of data points below the evanescencepoint 118, the following may be expected:

-   -   1. Linear relationship of FA-AI measurements.    -   2. A narrow and well-defined acoustic impedance for gas behind        the casing 22, although measured flexural attenuation values may        vary depending on the environment being logged, including casing        thickness and well fluid properties.    -   3. A narrow distribution of FA-AI values for liquids, with        likely uncertainty in the fluid properties and the potential for        more than one kind of liquid behind the casing 22, which may add        to the complexity of the resulting FA-AI values.

An example of actual experimental acoustic cement evaluation data,before parametric correction, appears in an x-y density distribution 140of FIG. 6. In the x-y density distribution 140 of FIG. 6, flexuralattenuation (FA) in units of dB/m (ordinate 42) is compared to acousticimpedance (AI) in units of MRayl (abscissa 144). A legend 145 shows thedata density of areas on the x-y density distribution 140. As seen inFIG. 6, a first cluster 146 of FA-AI data points may generallycorrespond to a measurement of gas behind the casing 22, a secondcluster 148 of FA-AI data points generally may relate to a liquidmeasured behind the casing 22, and a cluster 150 of FA-AI data pointsgenerally may relate to a solid behind the casing 22, though it may beseen that the flexural attenuation values beyond the evanescence point118 (e.g., around 4 MRayl) may not share the general pattern of thosedata points before the evanescence point 118. Single-measurement curves152 and 154 illustrate single-measurement density distributions forflexural attenuation and acoustic impedance, respectively. Local maximaof the curves 152 and 154 represent gases, liquids, and solids thatcorrespond to the clusters 146, 148, and 150. It may be appreciatedthat, since flexural attenuation is the sum of inside and outsideimpedance, if inside fluid is backed, then the origin of x-y plots is(0,0) and otherwise is not (e.g., as shown in FIG. 6).

As will be discussed further below, one type of solid-liquid-gas (SLG)model map that may be used to process the acoustic cement evaluationdata to identify solid, liquid, and gas behind the casing may be aconservative SLG model map. An example of a conservative SLG model map160 is shown in FIG. 7. The conservative SLG model map 160 of FIG. 7will be discussed briefly here to illustrate, for the purposes ofparametric correction of the acoustic cement evaluation data, arelationship between the FA-AI data points in discriminating betweensolid, liquid, and gas.

The conservative solid-liquid-gas (SLG) model map 160 of FIG. 7 plotsflexural attenuation (FA) in units of dB/cm (ordinate 162) againstacoustic impedance (Z) in units of MRayl (abscissa 164). The SLG modelmap 160 of FIG. 7 may be used to discriminate the FA-AI acoustic cementevaluation data points to be interpreted as gas, liquid, or solid behindthe casing 22. Before continuing, it should be noted that the SLG modelmap 160 of FIG. 7 may be developed using a computer model of data pointsthat are likely to be obtained in the wellbore 16 by propagating certainparametric assumptions and noise estimates through the computer model(e.g., a Monte Carlo simulation of the acoustic tool(s) 26 in thewellbore 16). The a priori parametric and/or data noise estimates usedto generate the conservative SLG model map 160 may be any suitableparametric and/or data noise estimates that, based on collections ofempirical data from various wells, would be understood to conservativelyclassify acoustic cement evaluation data points as solids, liquids, andgases. As will be discussed further below, changing the noise estimatesand/or parametric assumptions may produce other SLG model maps, such asa “tight” SLG model map that will be discussed below with reference toFIG. 21. In the SLG model map 160 of FIG. 7, data generally falling in afirst threshold range 166, having a nominal point 168, may be classifiedas gas. The first threshold range 166 may also be referred to in thisdisclosure as the gas threshold range 166. Data points falling within athreshold range 170, having a nominal point 172, may be classified asliquid. The threshold range 170 may also be referred to in thisdisclosure as the liquid threshold range 170. Points falling within athreshold range 174, around a nominal point 176, may be classified as asolid (e.g., cement). The threshold range 174 may also be referred to inthis disclosure as the solid threshold range 174. In the conservativeSLG model map 160 of FIG. 7, the linear relationship discussed abovewith reference to FIG. 5 may not immediately be apparent.

The solid-liquid-gas (SLG) model map 160 of FIG. 7 may be transformedinto an AI-AI SLG model map 190 of FIG. 8, which more clearlyillustrates the linear relationship between the pulse-echo-derivedacoustic impedance values and measured flexural attenuation valuesbeneath the evanescence point. The SLG model map 190 compares acousticimpedance derived from measurements of flexural attenuation in units ofMRayl (ordinate 192) and acoustic impedance measurements in units ofMRayl (abscissa 194). The AI-AI SLG model map 190 still includes a gasthreshold range 166 and nominal point 168 corresponding to gas behindthe casing 22, a liquid threshold range 170 and a nominal point 172corresponding to liquid behind the casing 22, and a solid thresholdrange 174 corresponding to solid material (e.g., cement) behind thecasing 22. Because the AI-AI SLG model map 190 is plotted in an AI-AIscale, when the parameters to the acoustic cement evaluation data arecorrectly chosen, the two acoustic impedance sets of data should aligngenerally along a unit slope 176 (i.e., a 45 degree line) passingthrough equal x-y values and the known expected nominal value points 168and 172.

The AI-AI SLG model map 190 thus may provide the expected nominal valuesthat the acoustic cement evaluation data may match when the parametersfor the acoustic cement evaluation data have been properly selected.Deviation or offset of the actually obtained acoustic cement evaluationdata and the expected acoustic cement evaluation data may implyparametric errors. For example, a deviation in the actually obtainedacoustic cement evaluation data from the ranges 166, 170, and 174 and/orthe nominal points 168 and 172, or a mismatch between the actuallyobtained acoustic impedance measurement and theflexural-attenuation-derived acoustic impedance measurement, at leastfor the subset of data points beneath the evanescence point 118, mayimply parametric errors. One possible parametric error may be an errorof the acoustic impedance of the fluid (Zmud) in the wellbore 16.Another possible parametric error may be an error in the calibration ofthe flexural attenuation measurement. Here, it may be noted thatdifferent parameter errors may affect the actually obtained acousticcement evaluation data in different ways. A Zmud parameterization errormay be amplified by a factor substantially larger than one, such as afactor of five, onto the acoustic impedance measurement. By contrast,such a Zmud parameterization error may be amplified in theflexural-attenuation-derived acoustic impedance Z(FA) by a factorapproaching one. On the other hand, the flexural attenuation calibrationmay apply to the flexural attenuation measurement, and thus may explainany offset occurring exclusively along the y-axis. By identifyingdiscrepancies between the actually obtained acoustic cement evaluationdata and the expected nominal values, these parametric errors may beidentified and a remedy may be attempted.

Indeed, the nominal points 168 and 172 in FIG. 8 occur along the unitslope line 176. It may be noted that the unit slope line 176 correspondsto points for which the values Z(FA) are equal to Z(AI). For valuescorresponding to gas, the acoustic impedance behavior is well defined.For this reason, as will be discussed below, the interval of acousticimpedance over which to perform parametric correction may be chosen tobe statistically relevant, and may be less than the full log of acousticimpedance data. It may noted that, for liquids, there may be someuncertainty of the a priori knowledge of the tool nominal values 168 and172, and therefore a potential for a mismatch between the assumed fluidof the initial parameterization of the acoustic cement evaluation dataand the actual fluid behind the casing 22. Indeed, more than one fluidmay be layered or may form a gradient of various fluids, throughout thecollection of the acoustic cement evaluation data in the wellbore 16. Adatabase of known behavior of fluid properties can help in reducinguncertainty.

Keeping the above in mind, an interval of acoustic cement evaluationdata that includes both flexural-attenuation-derived acoustic impedanceand pulse-echo-derived acoustic impedance data may be considered in anx-y (AI-AI) density distribution form. A subset of data points beneaththe evanescence point 118 may be used for the analysis of parametriccorrection because, beneath the evanescence point 118, the linearity andunit slope assumption of the AI-AI data is valid over the rangeassociated with the gas and liquid population. However, the processingbased on the corrected parameters can be applied to the entire datasetor some portion of the entire dataset, without regard to whether thedata points are above or below the evanescence point 118. As mentionedabove, the gas and liquid population of AI-AI data points may have a farmore precise behavior definition than the range of potential values forsolids that may be found behind the casing 22. In addition, the pointsof the acoustic cement evaluation data that may be examined in aparametric correction process may be those that exhibit at least twodistinct density distribution clouds of data below the evanescencepoint. These may include gas and liquid (G+L), liquid and solid (L+S),gas and solid (G+S) or gas, liquid, and solid (G+L+S). With more thanone distinct density distribution cloud of data points, at least one ofthese clouds (e.g., gas or liquid) may be anchored well to an expectednominal point, as will be described below. Moreover, from these distinctdensity distribution clouds, the nominal slope may be well defined inthe AI-AI plane and a trend line may be derived from these two or threedensity distribution clouds and their respective local maxima. In fact,in some embodiments, parametric corrections as discussed here may bedefined with minor user interaction and performed automatically by thedata processing system 38. In some embodiments, a user may select adepth interval over which to estimate and/or apply the parametriccorrection to the acoustic cement evaluation data. In other embodiments,a user may decide an offset or may augment an attempt automaticallygenerated by the data processing system 38 to cause the acoustic cementevaluation data to more closely align with the expected nominal values.

As shown in a flowchart 200 of FIG. 9, a collection of the acousticcement evaluation data over a suitable depth interval may be analyzed toidentify local maxima or centroids of clusters of an AI-AI x-y densitydistribution (block 202). The points that are considered for theanalysis of parametric correction may be beneath the evanescence point118 (block 203). When a correction is developed based on the analysis ofpoints below the evanescence point, the correction may be applied to theentire dataset, including points above the evanescence point. An exampleof an AI-AI x-y density distribution will be described in greater detailbelow with reference to FIG. 12.

Continuing with the flowchart 200 of FIG. 9, the data processing system38 may consider for the analysis of parametric correction whether thedata points are distributed generally along a unit slope (decision block204), whether the data points are distributed within an expectedsuitable solid-liquid-gas (SLG) range (decision block 206), whether themaxima have substantially equal x and y values (decision block 208),and/or whether the maxima or the centroids of the density distributionclusters are found at the expected nominal values (e.g., the nominalvalues 168 and 172 discussed above with reference to FIG. 8) (decisionblock 210). When the above criteria have been meet, the acoustic cementevaluation data may be understood to have been properly parameterized.As such, additional parametric correction may not be performed (block212). Otherwise, parametric correction may be performed on the acousticcement evaluation data (block 214).

As will be discussed below, the parametric correction of this disclosuremay take place in any suitable manner. One example appears in aflowchart 220 of FIG. 10. Here, the data processing system 38 mayreceive the acoustic cement evaluation data on which to perform acorrection (block 222). The largest population of data points (e.g., a“liquid” cluster or a “gas” cluster) may be identified as a first maximaand a smaller population may be identified as a second maxima (block224). In a first alternative path (ALT 1), if the first maxima is not atthe expected nominal point (decision block 226), an offset may bedetermined that causes the first maxima to reach the nominal point(block 228). The data processing system 38 further may verify that thiscorrection results in a unit slope and that the second maximum is closedto its corresponding nominal point (block 230). The data processingsystem 38 may implement the correction in any suitable manner using anentirety or just part of the dataset, which may include data points bothabove and below the evanescent point (block 231). If the first maxima isdetermined to be at the expected nominal point (decision block 226), noparametric correction may be applied or the second maxima may beconsidered instead (block 232).

Alternatively, the same exercise can be done starting with the secondmaxima instead of or in addition to the first maxima, as illustrated ina second alternative path (ALT 2). If the second maxima is not at itscorresponding nominal point (e.g., 168 or 172) (decision block 233), thedata processing system 38 may determine an offset that would cause thesecond maximum to be centered on the corresponding nominal point (block234). The data processing system further may verify that the correctionresults in a unit slope and that the first maximum remains near to itscorresponding nominal point (block 236). If the second maxima isdetermined to be at the expected nominal point (decision block 233), noparametric correction may be applied or the first maxima may beconsidered instead (block 238).

The processing system 38 may implement any of these corrections (block231) in the acoustic cement evaluation data in any suitable way.Moreover, the acts of block 231 may occur after the offsets for thefirst and/or second maximum have been determined (e.g., after the actsof block 228 and 234), or may occur when these offsets are determined.The corrections of block 231 may represent, for example, (1) applying amanual offset to the acoustic cement evaluation data and/or (2)adjusting the parameters affecting the acoustic cement evaluation datadirectly. With regard to the second example, the initial parameters maybe changed to second parameters that cause the acoustic cementevaluation data to more closely match the expected nominal values.

FIG. 11 illustrates an example of applying such offsets to perform aparametric correction of cement evaluation data as described in FIG. 10.In FIG. 11, a density distribution plot 250 comparesflexural-attenuation-derived acoustic impedance Z(FA) in units of MRayl(ordinate 252) to pulse-echo-derived acoustic impedance Z(AI) in unitsof MRayl (abscissa 254). In the example of plot 250, a gas cluster 146(G) having a centroids or local maximum 256 and a liquid (L) cluster 148having a centroids or local maximum 258 are adjusted to match theexpected nominal points 168 and 172 for gas and liquid, respectively.Each is shown in FIG. 11 as an “anchor point.” Before correction, thelocal maxima 256 and 258 are aligned in a non-unit slope 260. The maxima256 and 258 may be adjusted to the nominal points 168 and 172,respectively, to cause the data to exhibit a proper one-to-one x-yrelationship along the unit slope 176. As mentioned above, these offsetsmay be produced “manually,” in which the acoustic cement evaluation datais corrected without changing the underlying parameters that produce theoriginal, erroneous results. Additionally or alternatively, the dataprocessing system 38 may select a different parameterization until theacoustic cement evaluation data substantially matches the expectednominal values.

FIGS. 12 and 13 illustrate the method of FIGS. 4, 9, and 10 as appliedto experimental acoustic cement evaluation data. Specifically, FIG. 12illustrates an AI-AI x-y density distribution 270 comparingflexural-attenuation-derived acoustic impedance Z(FA) in units of MRayl(ordinate 272) to pulse-echo-derived acoustic impedance Z(AI) in unitsof MRayl (abscissa 274). A legend 145 represents data density. The AI-AIx-y density distribution 270 of FIG. 12 includes two identifiabledensity distribution clusters—a gas cluster 146 and a liquid cluster148—whose centroids or local maxima may be adjusted to align to thenominal gas and liquid points 168 and 172, respectively.

Correcting the data of FIG. 12 as indicated may produce a parametricallycorrected AI-AI x-y density distribution 280, which is shown in FIG. 13.In the AI-AI x-y density distribution 280 of FIG. 13,flexural-attenuation-derived acoustic impedance Z(FA) in units of MRayl(ordinate 282) is compared to pulse-echo-derived acoustic impedanceZ(AI) in units of MRayl (abscissa 284), in the same manner of FIG. 12. Alegend 145 represents the data density. In FIG. 13, the gas cluster 146now is substantially aligned with the gas nominal point 168. Likewise,the liquid cluster 148 is now substantially aligned with the liquidnominal point 172 along the unit slope line 176. This parametricallycorrected acoustic cement evaluation data may be used to more accuratelyidentify the characteristics of material behind the casing 22.

Parametric Correction of Single-Measurement Acoustic Cement EvaluationData

A single measurement of acoustic cement evaluation data—such as just theflexural attenuation data or just the acoustic impedance data—may alsobe parametrically corrected. Indeed, a similar approach can be carriedout using measurements of acoustic impedance alone or acoustic impedancemeasurement derived from flexural attenuation. This parametriccorrection may be distinguished from acoustic impedance“standardization” that may be carried out over known conditions, such asa known free-pipe interval of the wellbore 16 that includes liquid inthe annulus 20. Indeed, the parametric correction discussed hereinvolves analyzing the density distribution behavior of the acousticimpedance or the flexural-attenuation-derived acoustic impedance overany suitable interval, including the entire interval that is desired tobe examined to determine the material located behind the casing 22.

As shown by a flowchart 290 of FIG. 14, the single measurement ofacoustic cement evaluation data, such as acoustic impedance, flexuralattenuation, or flexural-attenuation-derived acoustic impedance(FA-derived AI) may be considered by the data processing system 38 forany suitable interval using data points beneath the evanescence point118 (block 292). The data processing system 38 may investigate thedensity distribution population distribution (block 294). The dataprocessing system 38 further may, if warranted, perform parametriccorrection to fit local maxima in the density distribution populationdistribution to expected nominal anchor points (block 296). It may beappreciated that the curves 152 and 154 of FIG. 6 represent examples ofsingle-measurement density distributions that may be used in parametriccorrection.

As shown in a flowchart 300 of FIG. 15, investigating the densitydistribution population distribution as described above with referenceto block 294 of FIG. 14, may take place as shown by a flowchart 300 ofFIG. 15. Examining a density distribution of a single measurement (e.g.,the curve 154 of acoustic impedance measurements shown in FIG. 6), localmaxima may be identified by the data processing system 38 (block 302).The processing system 38 may observe certain criteria, including whetherthe distribution of the single-measurement density distribution includesdata points distributed within the solid-liquid-gas (SLG) range(decision block 304), and whether the identified maxima occur atexpected nominal values (decision block 306). For instance, the localmaxima associated with gas may be centered on an acoustic impedancevalue of 0 MRayl.

When the criteria described in decision blocks 304 and 306 are met,parametric correction may not be performed (block 308). Otherwise, thedata processing system 38 may apply a parametric correction to thesingle-measurement acoustic cement evaluation data (block 310). Itshould be understood that the correction may occur in any suitablefashion. For instance, the data processing system 38 may adjust thevalues in substantially the same manner as described above withreference to FIG. 10, except that the data processing system 38 may notconsider the slope of a relationship between two measurements, butrather may focus on the relationship between the expected nominal pointsand the clusters.

Processing Acoustic Cement Evaluation Data Using a PrioriSolid-Liquid-Gas (SLG) Models

After obtaining the acoustic cement evaluation data, the data—whetherparametrically corrected or not—may be processed using any suitable apriori model. These may include, as discussed above with reference toFIG. 3, a conservative solid-liquid-gas (SLG) model, a “tight” SLG model84, and/or a flexural attenuation-evanescence-acoustic impedance(Flex-Eva-AI) SLG model 86. Although this disclosure describes thesemodels in particular, it should be appreciated that other models thatcan discriminate between solids, liquids, and/or gases behind the casing22 based on the acoustic cement evaluation data may be employed.

Conservative Solid-Liquid-Gas (SLG) Model

As discussed above, the conservative solid-liquid-gas (SLG) model 82referred to in the flowchart of FIG. 3, which may also be referred to asa conservative SLG model map, may provide helpful insight into theclassification of the material behind the casing 22. The conservativeSLG model 82 may enable operators to determine whether solid cement hasproperly set behind the casing 22 in the annulus 20, or whether somesort of fluid or gas is present instead. As noted above, FIG. 7represents a solid-liquid-gas (SLG) model map 160 that may be used toclassify materials behind the casing 22 at a given depth depending onthe acoustic cement evaluation data obtained by the acoustic tool(s) 26at that depth. As noted above, the SLG model map 160 plots flexuralattenuation in units of dB/cm (ordinate 162) against acoustic impedancein units of MRayl (abscissa 164). When the x-y point relating theflexural attenuation and acoustic impedance (AI or Z) at a particulardepth falls within the threshold range 166, the material located behindthe casing 22 at that depth may be classified as a gas. When the x-ypoint falls within the threshold range 170, the material located behindthe casing 22 at that depth may be classified as a liquid. When the x-ypoint falls within the threshold range 174, the material located behindthe casing 22 at that depth may be classified as a solid. Although theconservative SLG model map 160 is a model that has been used in thepast, here, the SLG model map 160 of FIG. 7 may be improved by using theparametrically corrected acoustic cement evaluation data and/or theposteriori refinement that will be discussed further below.

In one example, the conservative SLG model map 160 may be developedthrough an a priori computer simulation (e.g., a Monte Carlo simulation)of data points that may be measured by the acoustic tool(s) 26 relatingto solids, liquids, or gases that may appear in the wellbore 16, withnoise estimates and/or other parameters propagated through the model.The a priori parametric and/or data noise estimates used to generate theconservative SLG model map 160 may be any suitable parametric and/ordata noise estimates that, based on collections of empirical data fromvarious wells, would be understood to conservatively classify acousticcement evaluation data points as solids, liquids, and gases.

FIGS. 16 and 17 illustrate one example of determining the conservativeSLG model map 160 of FIG. 7. FIG. 16 illustrates a plot 311 of assumeddata points that, without any noise, could be detected by the acoustictools 26. The plot 311 relates flexural attenuation (Flex Att) in unitsof dB/cm (ordinate 312) against acoustic impedance (Z) in units of MRayl(abscissa 313). A first noiseless data cluster 314 illustrates datapoints that would represent a gas behind the casing 22, a secondnoiseless data cluster 315 illustrates data points that would representa liquid behind the casing 22, and a third noiseless data cluster 316represents data points that would represent a solid behind the casing22.

A plot of noisy data points, obtained by propagating a first noiseand/or parameter estimate relating to the wellbore 16 through thecomputer simulation, appears in a plot 318. The plot 318 relatesflexural attenuation (Flex Att) in units of dB/cm (ordinate 319) againstacoustic impedance (Z) in units of MRayl (abscissa 320). The first noiseand/or parameter estimate may be selected to be conservative withrespect to previously obtained empirical well logging data. Forinstance, the uncertainty of the parameters may be conservativelyselected to assume a vast range of possible conditions (e.g., from veryheavy to very light cement) and the noise estimate may assume thepossibility of logging through a very noisy environment (e.g., anoil-based well fluid). The resulting noisy data points include the firstcluster 146 relating to gas, the second cluster 148 relating to liquids,and the third cluster 150 relating to solids. Using these clusters, theSLG model map 160 of FIG. 7 may be determined.

Flexural Attenuation-Evanescence-Acoustic Impedance Solid-Liquid-Gas(SLG) Model

Other models may be used in addition to or as an alternative to theconservative solid-liquid-gas (SLG) model of FIG. 7. One such model isone that bifurcates its operation depending on the evanescence point. Inthis disclosure, such a model is referred to as a Flex-EVA-AI SLG model.An example of a Flex-EVA-AI SLG model map 320 appears in FIG. 18. TheFlex-EVA-AI SLG model map 320 compares flexural-attenuation-derivedacoustic impedance Z(FA) in units of MRayl (ordinate 322) plottedagainst pulse-echo-derived acoustic impedance Z(AI) in units of MRayl(abscissa 324). As discussed above, properly calibrated flexuralattenuation measurements generally increase monotonically with acousticimpedance measurements—until reaching an evanescence point in theacoustic impedance, which represents the transition from a solid that isable to maintain both a compressional and shear propagation to that ofjust shear propagation. For instance, as discussed above, the flexuralattenuation values of FIG. 5 increase monotonically with acousticimpedance until the pulse-echo-derived acoustic impedance reaches theevanescence point 118. Beyond the evanescence point 118, the measuredvalues of either flexural attenuation or acoustic impedance relate tothe presence of a solid behind the casing 22, even though the flexuralattenuation values no longer increase monotonically with the acousticimpedance. In some implementations of the acoustic tool(s) 26, theevanescence point may occur between approximately 3.5-4.5 MRayls and isa direct result of Snell's Law. Beyond the evanescence point, theflexural attenuation no longer monotonically increases with acousticimpedance, but in fact starts decreasing.

From FIG. 5, it also may be apparent that flexural attenuation on itsown may not provide a unique solution to the classification of amaterial behind the casing 22 as solid, liquid, or gas. The flexuralattenuation may use another measurement—here, the pulse-echo-derivedacoustic impedance—to provide an unambiguous answer. In essence, theadditional information that can be used to properly assign a flexuralattenuation data point measurement to a material state may be thedetermination of whether the corresponding pulse-echo-derived acousticimpedance value at the same depth is above or below the evanescencepoint. Thus, for a reading below the evanescence point, the flexuralattenuation or corresponding flexural-attenuation-derived acousticimpedance Z (AI). Indeed, for a reading below the evanescence point, theflexural attenuation or the transformed flexural-attenuation-derivedacoustic impedance Z (AI) may be directly used to analyze the materialin the annulus 20.

The Flex-EVA-AI solid-liquid-gas (SLG) model map 320 of FIG. 18 takesadvantage of this relationship. The Flex-EVA-AI SLG model map 320 isdivided into two segments, 326 and 328, that are separated at theevanescence point 118. In the segment 326, a one-dimensionalthresholding of the flexural attenuation or, in this case,flexural-attenuation-derived acoustic impedance Z(FA), may be used todiscriminate between solids, liquids, and gases behind the casing 22 inthe annulus 20. Thresholds in the flexural attenuation orflexural-attenuation-derived acoustic impedance Z(FA) may be used todesignate whether the material behind the casing 22 in the annulus 20 isa gas (330), a liquid (332), or a solid (334). In the segment 328 of theFlex-EVA-AI map 320, points beyond the evanescence point may beclassified as a solid (336).

The Flex-EVA-AI map 320 of FIG. 18 may leverage to a greater extent someof the benefits of the flexural attenuation measurement over theacoustic impedance measurement when lightweight materials are behind thecasing 22 in the annulus 20. These benefits of the flexural attenuationmeasurement over the acoustic impedance measurement may include betterprecision and sensitivity to variations in the annulus 20. This mayallow the Flex-EVA-AI map 320 to effectively have a larger effectivemeasurement area, and thus a reduced sensitivity to casing rugosity. TheFlex-EVA-AI map 320 may also provide reduced sensitivity to the wellfluid that pulse-echo-derived acoustic impedance, and any errors relatedto this parameter—either measured or estimated from a fluid database—mayincur.

In addition, the Flex-EVA-AI map 320 may be less complex and morestraightforward to implement than the SLG model map 160 of FIG. 7.Indeed, the Flex-EVA-AI map 320 may provide a binary discriminator inrelation to pulse-echo-derived acoustic impedance Z (AI). This mayreduce uncertainties and enable a refined approach to materialclassification in difficult logging conditions. Indeed, as illustratedin FIG. 18, the Flex-EVA-AI map 320 may provide a one-dimensionalthresholding, defined by two primary threshold cutoffs—(1) a gas toliquid threshold and (2) a liquid to solid threshold—along the ordinate322 representing the flexural attenuation-based axis.

The Flex-EVA-AI model of FIG. 18 may be determined and used asillustrated by a flowchart 340 of FIG. 19. Using flexural attenuationmeasurements or flexural-attenuation-derived acoustic impedance Z(FA)and pulse-echo-derived acoustic impedance Z (AI), the data processingsystem 38 may identify the evanescence point (block 342). A goodstarting point for identifying the evanescence point may be between 3.5and 4.5 MRayl, but this value may vary for various reasons includingchanges in behavior of the cement and the properties of the wellbore 16.Any suitable technique (e.g., a user-defined threshold and/or adata-driven threshold) may be used to identify the evanescence pointincluding identifying an inflection point of a density distribution offlexural attenuation values relative to pulse-echo-derived acousticimpedance values.

Using any suitable techniques, nominal data points of flexuralattenuation or flexural-attenuation-derived acoustic impedance Z(FA) maybe identified for gases and liquids (block 344). The nominal points maybe determined, for example, using database values of experimentallyobtained or simulated flexural attenuation values for different types ofmaterials behind the casing 22 in the annulus 20.

The data processing system 38 may determine nominal point thresholdsdefining the transition between flexural attenuation measurements fromgas to liquid and from liquid to solid (block 346). In one example, thegas-liquid threshold and liquid-solid threshold may be equal to therespective nominal values, plus some known measurement accuracy of thesevalues (e.g., nominal point+measurement accuracy).

The data processing system may define an x-y data point as a gas,liquid, or solid depending on whether the pulse-echo-derived acousticimpedance Z (AI) is above or below the evanescence point (decision block348). When the pulse-echo-derived acoustic impedance Z (AI) is below theevanescence point, the data processing system 38 may use the gas-liquidand liquid-solid thresholds for discriminating whether the materialbehind the casing 22 is a gas, liquid, or solid (block 350).Specifically, the data processing system 38 may assign the data point tobe a solid, liquid, or gas based on the threshold (block 352).

If the pulse-echo-derived acoustic impedance Z (AI) is above theevanescence point, the material behind the casing 22 can reliably bedefined as a solid. As such, the data processing system 38 may insurethat the data point meets solid criteria (e.g., that thepulse-echo-derived acoustic impedance Z (AI) is greater than or equal tothe liquid-solid threshold plus some value of measurement accuracy). Ifso, the data processing system 38 may assign the data point to be asolid (block 356). The data processing system 38 may repeat this processfor the acoustic cement evaluation data points and may display thesedata points in a well log track (block 358).

As an example, FIG. 20 provides a sample well log 370 with three tracks372, 374, and 376 over a depth interval of a test well from about150-350 meters. The first track 372 represents a well log track thatindicates whether a solid, liquid, or gas is likely to be disposedbehind the casing 22 based on the conservative solid-liquid-gas (SLG)model map of FIG. 7. The second track 374 represents a well log trackdetermined using the Flex-EVA-AI SLG model of FIG. 18, as carried out bythe flowchart 340 of FIG. 19. The third track 376 represents thepulse-echo-derived acoustic impedance Z (AI) over the depth interval.Three legends, 378, 382, and 380 indicate the information conveyed bythe three tracks 376, 374, and 372, respectively.

Here, between the depths 260-280 meters, the second track 374 moreclearly indicates the presence of solids behind the casing 22 than thefirst track 372 formed using the conservative SLG model. Note, however,that the Flex-EVA-AI model of FIG. 18 may have an even greater impact onevaluating lightweight cements.

Indeed, it may understood that defining the thresholds of the flexuralattenuation used in the Flex-EVA-AI model of FIG. 18 may be particularlychallenging when the fluid behind the casing 22 is particularly heavy,while the cement being used behind the casing 22 is particularly light.Under such conditions, defining the threshold in an a priori—that is,prior to logging—fashion may be useful, but may not reflect an optimalchoice for some conditions. As such, the parametric correction discussedabove may improve the a priori model of the Flex-EVA-AI model of FIG.18. In addition, as will be discussed further below, the Flex-EVA-AImodel may be further refined using posteriori information, which isinformation acquired during logging.

“Tight” Solid-Liquid-Gas (SLG) Model

Under certain conditions, a “tight” solid-liquid-gas (SLG) model mayprovide stronger discrimination of solids, liquids, and gases behind thecasing 22. In particular, when certain lightweight cements are used,often referred to as ultra-light cements, the data points of theacoustic cement evaluation data that define the presence of a liquidbehind the casing 22 may have a much more limited range than in otherSLG models. Indeed, a “tight” SLG model map 390 provides an example of atighter model the can be used to discriminate between solids, liquids,and gases behind the casing 22 in this way. In the tight SLG model map390 of FIG. 21, flexural attenuation or, in this case,flexural-attenuation-derived acoustic impedance Z(FA) in units of MRayl(ordinate 392) is plotted against pulse-echo-derived acoustic impedanceZ (AI) in units of MRayl (abscissa 394). As in the conservative SLGmodel of FIG. 7, the tight SLG model map 390 includes a threshold range166 of data points that relate to gas, a threshold range 170 thatcorrespond to liquid, and a threshold range 174 that correspond tosolids. Nominal points 168 and 172 still align along the unit slope 176.The ranges 166 and 170 corresponding to gas and liquid, however, may betighter than the conservative SLG model map of FIG. 7. In addition, thisallows, potentially, the definition of patchy dry debonding that mayoccur in a range 396.

The ranges 166, 170, and 174 of the tight SLG model map 390 may bedetermined in any suitable way. For example, the conservative SLG modelmap of FIG. 7 may be refined based on a priori values associated withwells with ultra light cement and/or heavy liquids. For instance, thetight SLG model map 390 may be determined by reducing noise assumptionsthat are propagated through a computer simulation (e.g., a Monte-Carlomodel). Additionally or alternatively, the tight SLG model map 390 maybe obtained by reducing the uncertainty of certain parameters used ingenerating the tight SLG model map 390, such as fluid density,compressional wave velocity (VP), fluid acoustic impedance (Zmud),and/or thickness of the casing 22. In other examples, the tight SLGmodel map 390 may be determined using a posteriori refinement from theacoustic cement evaluation data obtained from the wellbore 16 that isbeing evaluated, as will be discussed further below. In the tight SLGmodel map 390, the gas threshold range 166 is not directly adjacent tothe liquid threshold range 170. That is, unlike the conservative SLGmodel map 160 of FIG. 7, in the tight SLG model map 390 of FIG. 21, thegas threshold range 166 does not directly border a part of the liquidthreshold range 170. In this context, the term “directly adjacent” maybe understood to mean “not touching.” As seen in the tight SLG model map390, the gas threshold range 166 does not touch the liquid thresholdrange 170. Rather, there is a space between the gas threshold range 166and the liquid threshold range 170; when a data point falls in thisspace, it may be understood to most likely be tool noise and not torepresent either a liquid or a gas.

A plot 397 shown in FIG. 22 represents an example of simulated datapoints that may be used to generate the tight SLG model map 390. Theplot 397 may be obtained by propagating a noise estimate through acomputer simulation (e.g., a Monte Carlo simulation) of well conditionsbased on ideal data points from the plot 311 of FIG. 16. It may berecalled that these data points of the plot 311 of FIG. 16 can also beused to determine the conservative solid-liquid-gas (SLG) model map 160of FIG. 7 by propagating a first noise and/or parameter estimate throughthe computer simulation. As noted above, the first noise and/orparameter estimate may be selected to be conservative with respect topreviously obtained empirical well logging data. For instance, theuncertainty of the parameters may be conservatively selected to assume avast range of possible conditions (e.g., from very heavy to very lightcement) and the possibility of logging through a very noisy environment(e.g., an oil-based well fluid). As also noted above, the result ofpropagating the first noise estimate through the computer model may bethe plot 318 of FIG. 17, which can be used to define the SLG model mapof FIG. 7.

Propagating a second estimate through the computer simulation (e.g., aMonte Carlo simulation) of the well conditions with lower noiseassumptions and less parameter uncertainty, however, may produce theplot 397 of FIG. 22. For example, by reducing the amount of noise thatis estimated to occur in the measurements of the data points from theacoustic tool(s) 26, the computer simulation may produce tighter datapoint clouds that can form the basis of the “tight” SLG model map 390 ofFIG. 21. In the plot 397 of FIG. 22, flexural attenuation (Flex Att) inunits of dB/cm (ordinate 398) is plotted against acoustic impedance (Z)in units of MRayl (abscissa 399). The noisy data points produced by thelower noise estimate propagated through the computer simulation mayinclude the first cluster 146 relating to gas, the second cluster 148relating to liquids, and the third cluster 150 relating to solids.Indeed, as can be seen in FIG. 22, at least the data point clusters 146and 148—developed using this lower noise estimate—are much tighter thanthose shown in the plot 318 of FIG. 17, which was determined using ahigher noise estimate.

The noise estimate that is propagated through the computer simulation togenerate the plot 397 of FIG. 22, and subsequently the “tight” SLG modelmap 390 of FIG. 21, may be lower by any suitable amount than that usedto generate the plot 318 of FIG. 17, and subsequently the conservativeSLG model map 160 of FIG. 7. In one example, the noise estimate in they-axis used to generate the “tight” SLG model map 390 of FIG. 21 may belower by about a factor of two to four from that used to generate theconservative SLG model map 160 of FIG. 7. For example, a standarddeviation of estimated noise may be reduced by a factor of about up totwo to four. Even more, the reduction of estimated noise or parametricuncertainty may be up to approximately 3 standard deviations along thepulse-echo-derived acoustic impedance axis, and may be up toapproximately 6 standard deviations along the flexural attenuation orflexural-attenuation-derived acoustic impedance axis. The totalreduction in standard deviations of estimated noise and/or parametricuncertainty may be, in some cases, up to a total of 8. Parametricassumptions propagated through the computer simulation may be selectedto achieve the “tight” SLG model map 390 of FIG. 21. For instance, awell fluid density, a fluid compressional wave (VP), and/or a well fluidacoustic impedance may be selected using less uncertainty than used togenerate the conservative SLG model map 160 of FIG. 7.

Posteriori Refinement of a Priori Models

In many cases, the application of the acoustic cement evaluation data tovarious a priori models may be further refined to provide an even bettermanner of classifying the material behind the casing 22 in the annulus20 of the wellbore 16. Indeed, the conservative solid-liquid-gas (SLG)model map may remain a valuable aid to quickly classify zones of goodisolation (e.g., zones where substantially entirely properly cementedmaterial behind the casing 22), moderate isolation (e.g., zones where atleast some of the material behind the casing 22 in the annulus 20 isproperly cemented material), or free pipe (e.g., zones wheresubstantially no solid material in the analysis behind the casing 22).It may not be uncommon to log depth intervals of the wellbore 16 thatcontain primarily liquid or gas in the analysis behind the casing 22over a larger depth interval that is logged. These zones, in which thematerials detected in the acoustic cement evaluation data points may beliquids and/or gases, may be used to refine the a priori modelmeasurements by overlaying these solid and/or liquid data points overone of the SLG model maps discussed above.

In one example, shown as a flowchart 410 of FIG. 23, the data points ofacoustic cement evaluation data obtained at a depth interval whereliquid and/or gas is behind the casing 22 in the annulus 20 may beoverlaid onto one of the solid-liquid-gas (SLG) model maps discussedabove (block 412). For example, the data points from a depth interval ofliquid and/or gas in the annulus 20 behind the casing 22 may be overlaidonto the conservative SLG model map discussed above with reference toFIG. 7 above. The data points may be overlaid to form a densitydistribution plot, as will be discussed below.

The solid, liquid, and gas ranges (e.g., 166, 170, and 174) may begeographically refined (e.g., using a polygon- or polynomial-basedapproach as manually determined by a user) (block 414). The dataprocessing system 38 may regenerate the resulting solid-liquid-gas (SLG)to use the new newly defined boundaries to more precisely identifysolids, liquids, and gases over another interval (e.g., the entire depthinterval) where acoustic cement evaluation data has been obtained (block416). This refined SLG model map may be used to generate a final answerproduct (e.g., a well log indicating whether the acoustic cementevaluation data points obtained at various depths in the wellbore 16indicate a solid, liquid, and/or gas behind the casing 22 in the annulus20.) The refined SLG model map may be more precise and/or accurate thanthe initial SLG model map.

In another example, shown as a flowchart 420 of FIG. 24, the data pointsfrom the liquid and/or gas interval of the well may be overlaid onto aSLG model map (block 422), and a statistical analysis may be used torefine the data points using a computer simulation (block 424). Forexample, the statistical analysis may refine the input to a Monte-Carlosimulation that is used in an SLG model mapping in the manner discussedabove with reference to the “tight” SLG model. The data processingsystem 38 may regenerate the resulting solid-liquid-gas (SLG) to use thenew newly defined model (block 426). As before, the refined SLG modelmap may be more precise and/or accurate than the initial SLG model map.

FIGS. 22 and 23 illustrate examples of posteriori refinement asdescribed with reference to FIGS. 20 and/or 21. FIG. 25 illustrates adensity map 430 of acoustic cement evaluation data plotted asflexural-attenuation-derived acoustic impedance Z(FA) in units of MRayls(ordinate 432) and pulse-echo-derived acoustic impedance Z(AI) in unitsof MRayls (abscissa 434). Here, a conservative model of SLG isdisplayed, including a gas threshold range 166, a liquid threshold range170, and a solid threshold range 174. The unit slope line 176 is alsoshown. A density mapping 436 of data points correlated with a depthinterval of the wellbore 16 in which liquid and/or gas are presentbehind the casing 22 in the annulus 20 of the wellbore 16. As seen inthe example of FIG. 25, the data points appear to correspond to liquid,but the points do not extend into a range 438 where, if the SLG modelmap properly identified liquids, the data points would be expected toappear. This suggests that the conservative SLG model map may beill-suited for mapping this particular well. As such, a user may selectanother a priori mapping that might be better suited.

A plot 440 of FIG. 26 illustrates an improved solid-liquid-gas (SLG) mapthat has been refined using the posteriori knowledge shown above. In theplot 440, flexural attenuation-derived acoustic impedance Z(FA) in unitsin MRayls (ordinate 442) is plotted against pulse-echo-derived acousticimpedance Z(AI) in units of MRayls (abscissa 444). Here, a “tight” SLGmodel map results. When the data density 436 is overlaid on the tightSLG model map, it may apparent that the data more closely correlate tothe liquid threshold range 170 of the tight SLG model map than thecorresponding liquid threshold range 170 in the conservative SLG modelmap shown in FIG. 25. As such, the tight SLG model map shown in FIG. 26may be better suited to determine whether solids, liquids, or gases arepresent behind the casing 22 in the annulus 20.

Further refinements are possible, including further statistical analysisto determine an even more appropriate SLG model mapping using suchposteriori values. For instance, the liquid threshold range 170 shown inFIG. 26 may be further varied to more closely match the actual valuesthat have been obtained through the depth interval of the wellbore whereliquid is determined to be behind the casing 22 in the annulus 20.

The specific embodiments described above have been shown by way ofexample, and it should be understood that these embodiments may besusceptible to various modifications and alternative forms. It should befurther understood that the claims are not intended to be limited to theparticular forms disclosed, but rather to cover modifications,equivalents, and alternatives falling within the spirit and scope ofthis disclosure.

1. A method comprising: obtaining acoustic cement evaluation data pointsderiving from one or more acoustic downhole tools used in a wellborehaving a casing; processing the acoustic cement evaluation data pointsusing a solid-liquid-gas model to assign at least some of the acousticcement evaluation data points to a material of solid, liquid, or gas inan annulus of the wellbore behind the casing, wherein thesolid-liquid-gas model comprises: a tight solid-liquid-gas model inwhich a gas threshold range is not directly adjacent to a liquidthreshold range; or a solid-liquid-gas model that considers flexuralattenuation only when a pulse-echo-derived acoustic impedance is belowan evanescence point; or both.
 2. The method of claim 1, wherein theacoustic cement evaluation data points that are obtained derive from oneor more flexural attenuation measurements and one or more acousticimpedance measurements.
 3. The method of claim 1, wherein the gasthreshold range of the tight solid-liquid-gas model is tighter than acorresponding gas threshold range used in a conservativesolid-liquid-gas model and wherein the liquid threshold range of thetight solid-liquid-gas range is tighter than a corresponding liquidthreshold range used in the conservative solid-liquid-gas range.
 4. Themethod of claim 1, wherein the tight solid-liquid-gas model comprises arange not providing a threshold indication of liquid, solid, or gas, therange being disposed between the gas threshold range and the liquidthreshold range and corresponding to patchy dry debonding of cementbehind the casing.
 5. The method of claim 1, comprising generating thetight solid-liquid-gas model, wherein the tight solid-liquid-gas modelis generated at least in part by reducing noise properties propagatedthrough another solid-liquid-gas model to generate the tightsolid-liquid-gas model.
 6. The method of claim 1, comprising generatingthe tight solid-liquid-gas model, wherein the tight solid-liquid-gasmodel is generated at least in part by reducing an uncertainty value ofa parameter used by another solid-liquid-gas model to generate the tightsolid-liquid-gas model.
 7. The method of claim 6, wherein the parameterfor which the uncertainty value is reduced comprises a well fluiddensity, a fluid compressional wave (VP), a well fluid acousticimpedance, or any combination thereof.
 8. The method of claim 1,comprising performing a posteriori refinement of the solid-liquid-gasmodel.
 9. One or more tangible, non-transitory computer-readable mediastoring instructions to: receive data points, each data point comprisinga first component based on measured flexural attenuation in a wellhaving a casing and a second component based on pulse-echo-derivedacoustic impedance in the well having the casing; assign at least somedata points having a second component value at or above an evanescencepoint to indicate that a material behind the casing is solid; and assignat least some data points having a second component value below theevanescence point to indicate that the material behind the casing issolid, liquid, or gas depending at least in part on a value of the firstcomponent.
 10. The computer-readable media of claim 9, wherein the firstcomponent comprises a flexural attenuation value.
 11. Thecomputer-readable media of claim 9, wherein the first componentcomprises an acoustic impedance value derived from a flexuralattenuation value.
 12. The computer-readable media of claim 9, whereinthe instructions to assign at least some data points having a secondcomponent value at or above an evanescence point to indicate that amaterial behind the casing is solid comprise instructions to verify thatthe second component value is greater than a liquid-solid thresholdassociated with the second component plus a value of measurementaccuracy.
 13. The computer-readable media of claim 9, comprisinginstructions to: determine the evanescence point; determine a firstnominal first component point corresponding to gas behind the casing;determine a second nominal first component point corresponding to liquidbehind the casing; determine a gas-liquid threshold based at least inpart on the first nominal first component point; and determine aliquid-solid threshold based at least in part on the second nominalfirst component point; wherein the instructions to assign the datapoints having the second component value below the evanescence point toindicate that the material behind the casing is solid, liquid, or gasbased at least in part on a relationship of the value of the firstcomponent to the gas-liquid threshold or the liquid-solid threshold, orboth.
 14. The computer-readable media of claim 13, wherein theevanescence point is determined to be an acoustic impedance valuebetween approximately 3.5 and 4.5 MRayls.
 15. The computer-readablemedia of claim 13, wherein: the gas-liquid threshold is determined byadding a measurement accuracy to the first nominal first componentpoint; or the liquid-solid threshold is determined by adding ameasurement accuracy to the second nominal first component point; or acombination thereof.
 16. A method comprising: receiving acoustic cementevaluation data points deriving from one or more acoustic tools used ina well having a casing; processing the acoustic cement evaluation datapoints using one or more initial solid-liquid-gas models to indicatewhen a solid, liquid, or gas is likely behind the casing; performing aposteriori refinement of the one or more initial solid-liquid-gas modelsto determine a refined solid-liquid-gas model that is more precise ormore accurate, or more precise and more accurate, than the one or moreinitial solid-liquid-gas models; and processing the acoustic cementevaluation data points using the refined solid-liquid-gas model.
 17. Themethod of claim 16, wherein the one or more solid-liquid-gas modelscomprises: a conservative solid-liquid-gas model comprising a first gasthreshold range, a first liquid threshold range, and a first solidthreshold range; a tight solid solid-liquid-gas model comprising asecond threshold range, a second liquid threshold range, and a secondsolid threshold range, at least one of which is tighter than thecorresponding first threshold ranges of the conservativesolid-liquid-gas model; or a solid-liquid-gas model that considersflexural attenuation only when a pulse-echo-derived acoustic impedanceis below an evanescence point; or any combination thereof.
 18. Themethod of claim 16, wherein performing the posteriori refinementcomprises: overlaying a density distribution of at least some of theacoustic cement evaluation data points onto a map of the one or moreinitial solid-liquid-gas models; and geographically refiningsolid-liquid-gas threshold boundaries of the map of the one or moreinitial solid-liquid-gas models to determine the refinedsolid-liquid-gas model.
 19. The method of claim 18, wherein thesolid-liquid-gas threshold boundaries are geographically refined using apolygon approach, polynomial approach, or both polygon and polynomialapproach.
 20. The method of claim 16, wherein performing the posteriorirefinement comprises: overlaying a density distribution of the acousticcement evaluation data points onto a map of the one or more initialsolid-liquid-gas models; and applying a statistical analysis of theacoustic cement evaluation data points to determine the refinedsolid-liquid-gas model.